AMATH/ATMOS 505/OCEAN 511
Waves
Try not to splash too much!
If any instructions for wave generation are unclear, please ask for a demo.
Propagating waves
In the long tank, dip the wooden paddle to about half the depth of the water. Move it back and
forth a couple of times then stop, to create a finite packet or group of waves.
1. Observe. Explain what you observe in at least three sentences.
2. Repeat the paddle movement. This time have one person follow, with their finger, the leading
edge of the disturbance, and have another person follow a wave crest in the wave packet. Does
the crest near the leading edge of the wave packet propagate all the way to the other side of
the tank? What happens to it? (group velocity vs. phase velocity).
3. Now create a bore. “Pile up” the water on one end of the tank then release, sending a step
function of water out from the end of the tank. Observe. What happens to the bore after it
reflects from the ends of the tank a few times? You may think of this in terms of the shape
it starts with versus the shape you notice after a few bounces.
4. Why do you think this (what you observe in # 3) happens?
Standing waves
In the (approximately) 4 foot tank, use the paddle to make a standing wave, i.e. one whose pattern
does not change over time. Crests and troughs will alternate in any given location. It may be
helpful to aim to create 2 wavelengths (2 crests and 2 troughs) in the tank.
5. Note how the resistance changes depending on whether you are forcing at the same frequency
as the standing wave or not. Be sure to let others in the group try this.
Standing wave-particle trajectory
In the narrow taller tank, first stir up the particles from the bottom of the tank, then use the paddle
to make a standing wave of exactly 1 wavelength in the tank.
6. Sketch the particle trajectories. Compare this to Figure 7.14 in Kundu.
7. How do they compare to the trajectories you expect in a traveling wave? (Kundu Fig 7.6)
Propagating waves against a mean flow
In the recirculating flume with the large mountain.
8. Use the paddle to make propagating waves from upstream of the mountain, towards the
mountain. How far do these waves travel?
9. Now make propagating waves from the downstream side of the mountain, back towards the
mountain. How far do these waves go? What factor is limiting the wave propagation?
10. If you have time, note the change in wavenumber k(x) as the waves approach the mountain.
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